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scmbradley comments on Decision Theories: A Less Wrong Primer - Less Wrong
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That's one valid way of looking at the distinction.
CDT allows the causal link from its current move in chess to its opponent's next move, so it doesn't view the two as independent.
In Newcomb's Problem, traditional CDT doesn't allow a causal link from its decision now to Omega's action before, so it applies the independence assumption to conclude that two-boxing is the dominant strategy. Ditto with playing PD against its clone.
(Come to think of it, it's basically a Markov chain formalism.)
So these alternative decision theories have relations of dependence going back in time? Are they sort of couterfactual dependences like "If I were to one-box, Omega would have put the million in the box"? That just sounds like the Evidentialist "news value" account. So it must be some other kind of relation of dependence going backwards in time that rules out the dominance reasoning. I guess I need "Other Decision Theories: A Less Wrong Primer".